Hierarchical Modelling of Crossing Fibres in the White Matter

Abstract

While diffusion MRI is typically used to estimate microstructural properties of tissue in volumetric elements (voxels), more specificity can be obtained by separately modelling the properties of individual fibre populations within a voxel. In the context of cross-subjects modelling, these so-called fixel-based analyses require identifying equivalent fibre populations. This is usually done post-hoc, after estimating fibre orientations for individual subjects independently and subsequently matching the fixels between subjects. This approach can fail due to individual differences in fibre orientation distributions. Here, we introduce a hierarchical framework for fitting crossing fibre models to diffusion MRI data in a population of subjects. This hierarchical setup guarantees that the crossing fibres are consistent by construction and, therefore, comparable across subjects. We propose an expectation-maximisation approach to fit the model, which can scale to large numbers of subjects. This approach produces a crossing-fibre white matter fibre template, which can be used to estimate fibre-specific parameters that are consistent across subjects and, hence, can be used in fixel-based statistical analyses.